Question

A string of length $20cm$ and linear mass density $0.4g/cm$ is fixed at both ends and is kept under a tension of $16N$. A wave pulse is produced at $t=0$ near an end as shown in figure which travels towards the other end. The string have the shape shown in the figure again in $2\times {10}^{-x}sec$. Find $x$.

• A. $1$
  
• B. $2$
  
• C. $8$
  
• D. $3$
  

Answer 1

The correct option is B $2$

Given : $T=16$ N $L=0.2$ m $\mu =0.4$ g/cm $=0.04$ kg/m

Velocity of wave $v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{16}{0.04}}=20$ m/s

Time after which the string has the same shape $t=\frac{2L}{v}$

$\therefore$ $t=\frac{2\left(0.2\right)}{20}=2\times {10}^{-2}$ s $⟹x=2$